A295878 Multiplicative with a(p^(2e)) = 1, a(p^(2e-1)) = prime(e).

1, 2, 2, 1, 2, 4, 2, 3, 1, 4, 2, 2, 2, 4, 4, 1, 2, 2, 2, 2, 4, 4, 2, 6, 1, 4, 3, 2, 2, 8, 2, 5, 4, 4, 4, 1, 2, 4, 4, 6, 2, 8, 2, 2, 2, 4, 2, 2, 1, 2, 4, 2, 2, 6, 4, 6, 4, 4, 2, 4, 2, 4, 2, 1, 4, 8, 2, 2, 4, 8, 2, 3, 2, 4, 2, 2, 4, 8, 2, 2, 1, 4, 2, 4, 4, 4, 4, 6, 2, 4, 4, 2, 4, 4, 4, 10, 2, 2, 2, 1, 2, 8, 2, 6, 8, 4, 2, 3, 2, 8, 4, 2, 2, 8, 4, 2, 2, 4, 4, 12

Offset: 1

Author

Antti Karttunen, Nov 29 2017

Keywords

• nonn
• mult

Comments

This sequence can be used as a filter. It matches at least to the following sequence, as for all i, j:

a(i) = a(j) => A162642(i) = A162642(j), as A162642(n) = A001222(a(n)).

a(i) = a(j) => A056169(i) = A056169(j), as A056169(n) = A007814(a(n)).

a(i) = a(j) => A295883(i) = A295883(j), as A295883(n) = A007949(a(n)).

a(i) = a(j) => A295662(i) = A295662(j).

a(i) = a(j) => A295664(i) = A295664(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A294873, A295879.

Programs

Mathematica

Array[Apply[Times, FactorInteger[#] /. {p_, e_} /; p > 0 :> Which[p == 1, 1, EvenQ@ e, 1, True, Prime[(e + 1)/2]]] &, 120] (* Michael De Vlieger, Nov 29 2017 *)

Formula

a(1) = 1; for n>1, if n = Product prime(i)^e(i), then a(n) = Product prime((e(i)+1)/2)^A000035(e(i)).